Sewage is the municipal waste matter that is carried away in sewers and drains. It includes both liquid and solid wastes rich in organic matter and microbes. Many of these microbes are pathogenic and can cause several water-borne diseases. Sewage water is a major cause of polluting drinking water. Hence it is essential that sewage water is properly collected treated and disposed.


A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).
There are several valuable microorganisms that are beneficial to humans in various manners such as: